Case Study 2: Fourth Down Decision Analysis for a Championship Team
Introduction
State University finished the regular season 11-1 and earned a spot in the conference championship game. As part of their preparation, the coaching staff wants a comprehensive analysis of their fourth-down decision-making throughout the season.
The analytics department has been tasked with: 1. Auditing all fourth-down decisions for optimality 2. Quantifying points gained/lost from decision quality 3. Identifying systematic tendencies 4. Providing actionable recommendations for the championship game
Background
Team Profile
State University Offense: - Points per game: 34.2 (12th nationally) - Yards per play: 6.4 - Red zone TD rate: 68% - Third-down conversion rate: 44% - Fourth-down conversion rate: 62% (12/15 attempts)
State University Special Teams: - Field goal accuracy: 84% (21/25) - FG accuracy 40+: 75% (6/8) - Punting average (gross): 43.8 yards - Punting average (net): 40.2 yards - Opponent punt return average: 6.8 yards
State University Defense: - Points per game allowed: 18.5 - Yards per play allowed: 4.9 - Red zone TD rate allowed: 52% - Third-down conversion allowed: 32%
Fourth Down Decision Framework
For each fourth-down play, we calculate the expected points (EP) for three options:
- Go for it: EP = P(convert) × EP(success) + (1 - P(convert)) × EP(failure)
- Field goal: EP = P(make) × 3 + (1 - P(make)) × EP(miss position)
- Punt: EP = EP(opponent's starting position after punt)
The optimal decision is the one with the highest expected points.
Season Data Collection
All Fourth-Down Situations (52 total)
Over 12 games, State University faced 52 fourth-down situations:
| Category | Count |
|---|---|
| Went for it | 15 |
| Attempted FG | 25 |
| Punted | 12 |
Detailed Decision Log
Game 1 vs. Eastern State (W 35-14)
| Q | Time | Field Pos | Distance | Decision | Optimal | Result |
|---|---|---|---|---|---|---|
| 2 | 8:22 | Opp 35 | 4th & 2 | Punt | Go | Downed at 8 |
| 3 | 4:15 | Opp 28 | 4th & 6 | FG (45 yd) | FG | Made |
| 4 | 10:02 | Opp 42 | 4th & 1 | Go | Go | Converted |
Game 2 vs. Northern Tech (W 28-24)
| Q | Time | Field Pos | Distance | Decision | Optimal | Result |
|---|---|---|---|---|---|---|
| 1 | 2:45 | Opp 38 | 4th & 3 | Punt | Go | TB, Opp 25 |
| 2 | 0:45 | Opp 25 | 4th & 4 | FG (42 yd) | Go | Made |
| 3 | 6:18 | Opp 31 | 4th & 2 | Go | Go | Failed |
| 4 | 2:12 | Opp 18 | 4th & 3 | FG (35 yd) | FG | Made |
Game 3 vs. Midwest University (W 42-17)
| Q | Time | Field Pos | Distance | Decision | Optimal | Result |
|---|---|---|---|---|---|---|
| 1 | 5:30 | Opp 44 | 4th & 1 | Go | Go | Converted |
| 2 | 11:22 | Opp 8 | 4th & G | FG (25 yd) | Go | Made |
Game 4 vs. Southern State (W 31-28)
| Q | Time | Field Pos | Distance | Decision | Optimal | Result |
|---|---|---|---|---|---|---|
| 2 | 3:45 | Opp 36 | 4th & 4 | Punt | Go | Opp 12 |
| 2 | 0:08 | Opp 22 | 4th & 3 | FG (39 yd) | Go | Made |
| 3 | 8:15 | Opp 45 | 4th & 2 | Go | Go | Converted |
| 4 | 1:45 | Own 35 | 4th & 8 | Punt | Punt | Opp 22 |
Game 5 vs. Western College (W 45-21)
| Q | Time | Field Pos | Distance | Decision | Optimal | Result |
|---|---|---|---|---|---|---|
| 1 | 8:02 | Opp 32 | 4th & 1 | Go | Go | Converted |
| 3 | 5:45 | Opp 28 | 4th & 5 | FG (45 yd) | Go | Made |
Game 6 vs. Rival University (L 24-27)
| Q | Time | Field Pos | Distance | Decision | Optimal | Result |
|---|---|---|---|---|---|---|
| 1 | 3:22 | Opp 41 | 4th & 3 | Punt | Go | Opp 8 |
| 2 | 5:15 | Opp 35 | 4th & 2 | Punt | Go | Opp 5 |
| 3 | 10:45 | Opp 29 | 4th & 4 | FG (46 yd) | Go | Missed |
| 4 | 4:22 | Opp 38 | 4th & 5 | Punt | Go | Opp 12 |
| 4 | 0:38 | Opp 32 | 4th & 6 | Go | Go | Failed |
Games 7-12 Summary:
| Game | 4th Downs | Went For It | Optimal Decisions | Key Miss |
|---|---|---|---|---|
| 7 | 5 | 1 | 3/5 | Punted 4th & 1 at Opp 45 |
| 8 | 3 | 1 | 2/3 | FG instead of Go at Opp 33 |
| 9 | 4 | 2 | 3/4 | Punted 4th & 2 at midfield |
| 10 | 5 | 1 | 2/5 | Multiple conservative punts |
| 11 | 4 | 2 | 4/4 | None |
| 12 | 6 | 2 | 4/6 | FG instead of Go at Opp 30 |
Analysis
Overall Decision Quality
Season Summary:
| Metric | Value |
|---|---|
| Total 4th downs | 52 |
| Optimal decisions | 32 |
| Suboptimal decisions | 20 |
| Decision quality rate | 61.5% |
Breakdown by Decision Type:
| Decision | Count | Optimal | Rate |
|---|---|---|---|
| Went for it | 15 | 13 | 86.7% |
| Field goal | 25 | 15 | 60.0% |
| Punt | 12 | 4 | 33.3% |
Points Impact Analysis
Expected Points Lost from Suboptimal Decisions:
For each suboptimal decision, we calculate: EP Lost = EP(optimal) - EP(chosen)
Detailed Analysis of Costly Decisions:
| Game | Situation | Chosen | Optimal | EP Lost |
|---|---|---|---|---|
| 1 | Opp 35, 4th & 2 | Punt | Go | 0.8 |
| 2 | Opp 38, 4th & 3 | Punt | Go | 0.6 |
| 2 | Opp 25, 4th & 4 | FG | Go | 0.4 |
| 3 | Opp 8, 4th & G | FG | Go | 0.7 |
| 4 | Opp 36, 4th & 4 | Punt | Go | 0.5 |
| 4 | Opp 22, 4th & 3 | FG | Go | 0.5 |
| 5 | Opp 28, 4th & 5 | FG | Go | 0.3 |
| 6 | Opp 41, 4th & 3 | Punt | Go | 0.7 |
| 6 | Opp 35, 4th & 2 | Punt | Go | 0.9 |
| 6 | Opp 29, 4th & 4 | FG | Go | 0.6 |
| 6 | Opp 38, 4th & 5 | Punt | Go | 0.5 |
| 7 | Opp 45, 4th & 1 | Punt | Go | 1.2 |
| 8 | Opp 33, 4th & 3 | FG | Go | 0.5 |
| 9 | 50, 4th & 2 | Punt | Go | 0.8 |
| 10 | Opp 40, 4th & 2 | Punt | Go | 0.9 |
| 10 | Opp 35, 4th & 3 | Punt | Go | 0.8 |
| 10 | Opp 42, 4th & 1 | FG | Go | 0.6 |
| 12 | Opp 30, 4th & 2 | FG | Go | 0.7 |
| 12 | Opp 38, 4th & 4 | Punt | Go | 0.5 |
| 12 | Opp 44, 4th & 1 | FG | Go | 0.4 |
Total Expected Points Lost: 12.9 points
Over 12 games, this represents approximately 1.1 expected points lost per game due to suboptimal fourth-down decisions.
Pattern Analysis
Conservative Bias Identification:
| Optimal Decision | Times Optimal | Times Chosen | Compliance |
|---|---|---|---|
| Go for it | 35 | 15 | 42.9% |
| Field goal | 15 | 25 | 166.7%* |
| Punt | 2 | 12 | 600.0%* |
*Values over 100% indicate over-selection relative to optimal
Key Finding: State University shows a strong conservative bias: - Goes for it only 43% of the time when optimal - Kicks field goals 67% more often than optimal - Punts 6x more often than optimal
Situational Tendencies
By Field Position:
| Zone | 4th Downs | Go Rate | Optimal Go Rate | Gap |
|---|---|---|---|---|
| Opp 0-10 | 4 | 50% | 75% | -25% |
| Opp 11-25 | 12 | 17% | 50% | -33% |
| Opp 26-40 | 18 | 28% | 78% | -50% |
| Opp 41-50 | 10 | 40% | 90% | -50% |
| Own 40-50 | 5 | 40% | 60% | -20% |
| Own 0-39 | 3 | 0% | 0% | 0% |
Greatest Gap: The opponent's 26-50 zone shows the largest discrepancy between actual and optimal go-for-it rates. This is the "no-man's land" where the team is too far for a comfortable field goal but too close to give up on scoring.
By Distance:
| Distance | 4th Downs | Go Rate | Optimal Go Rate | Gap |
|---|---|---|---|---|
| 4th & 1 | 12 | 58% | 92% | -34% |
| 4th & 2 | 14 | 36% | 79% | -43% |
| 4th & 3 | 10 | 20% | 60% | -40% |
| 4th & 4 | 8 | 25% | 50% | -25% |
| 4th & 5+ | 8 | 13% | 25% | -12% |
Key Finding: Short-yardage situations (4th & 1-2) show the largest missed opportunities. The team should go for it ~85% of the time on 4th & 1-2 in opponent territory.
By Score Differential:
| Score Context | 4th Downs | Go Rate | Notes |
|---|---|---|---|
| Leading 14+ | 10 | 10% | Very conservative when ahead |
| Leading 1-13 | 15 | 27% | Moderately conservative |
| Tied | 12 | 33% | Closer to optimal |
| Trailing 1-13 | 11 | 45% | More aggressive when behind |
| Trailing 14+ | 4 | 75% | Forced aggression |
Pattern: The coaching staff becomes appropriately aggressive only when trailing significantly. Conservative play while leading may be costing opportunities to extend leads.
Game 6 Deep Dive: The Loss
The only loss came against Rival University, 24-27. Let's examine the fourth-down decisions:
Situation 1: Q1, 3:22, Opp 41, 4th & 3 - Decision: Punt (downed at Opp 8) - Optimal: Go for it - EP Analysis: - Go: 0.56 × 2.3 + 0.44 × 1.2 = 1.82 - Punt: 0.9 (opponent at their 8 = -0.9 EP for them = +0.9 for us) - EP Lost: 0.92 - Result: Opponent drove 92 yards for touchdown
Situation 2: Q2, 5:15, Opp 35, 4th & 2 - Decision: Punt (downed at Opp 5) - Optimal: Go for it - EP Analysis: - Go: 0.62 × 2.0 + 0.38 × 0.8 = 1.54 - Punt: 0.6 - EP Lost: 0.94 - Result: Opponent punted, field position battle
Situation 3: Q3, 10:45, Opp 29, 4th & 4 - Decision: FG (46 yards, missed) - Optimal: Go for it - EP Analysis: - Go: 0.48 × 2.5 + 0.52 × 0.5 = 1.46 - FG: 0.65 × 3 + 0.35 × 1.2 = 2.37 - Actually, with 65% make rate, FG might be optimal here...
Let me recalculate. The kicker had shown 75% on 40+ yard kicks (6/8). Using team-specific rate: - FG: 0.75 × 3 + 0.25 × 1.2 = 2.55
This was actually close to optimal. However, the miss was costly.
Situation 4: Q4, 4:22, Opp 38, 4th & 5 - Decision: Punt (downed at Opp 12) - Optimal: Go for it - EP Analysis: - Go: 0.42 × 2.1 + 0.58 × 0.9 = 1.40 - Punt: 0.7 - EP Lost: 0.70 - Context: Down 3 points with 4+ minutes left - aggressive play warranted
Situation 5: Q4, 0:38, Opp 32, 4th & 6 - Decision: Go for it (failed) - Optimal: Go for it - Analysis: Correct decision, unsuccessful execution
Game 6 Summary: - Total EP lost from suboptimal decisions: ~2.5 points - Final margin: 3 points - Conclusion: Conservative decision-making may have directly contributed to the loss
Championship Game Recommendations
Based on season-long analysis, here are specific recommendations:
Recommendation 1: Increase Aggression in No-Man's Land
Current: 28% go-for-it rate at opponent's 26-40 Recommended: 65%+ go-for-it rate at opponent's 26-40
Specific Rules: - 4th & 1-2 at opponent's 26-40: Go for it unless trailing by 7+ in final 2 minutes - 4th & 3 at opponent's 26-40: Go for it if not in FG range (<45 yards) - 4th & 4 at opponent's 26-40: Evaluate based on down/distance conversion history
Recommendation 2: Short Yardage Aggression
Current: 58% on 4th & 1, 36% on 4th & 2 Recommended: 90%+ on 4th & 1, 75%+ on 4th & 2
Justification: - Team's conversion rate: 62% overall, higher on short yardage - Expected value strongly favors going for it in most field positions - Risk of punt/FG leaving points on the field
Recommendation 3: Reduce Punting from Opponent Territory
Current: 12 punts from opponent territory all season Recommended: Maximum 2-3 punts from opponent territory per season
The only justified punts from opponent territory: - 4th & 10+ with no FG opportunity - Leading in final 3 minutes and pinning deep is strategically valuable - Weather conditions severely limiting conversion probability
Recommendation 4: Context-Specific FG Decisions
When to kick field goals: - Inside opponent's 25-yard line when distance is 4th & 5+ - When FG wins or ties the game in final minutes - When weather significantly reduces conversion probability
When to go for it instead of FG: - 4th & goal from inside the 5-yard line - 4th & 1-3 from opponent's 25-35 (outside comfortable FG range) - When leading by 4-7 points (TD extends lead more than FG)
Recommendation 5: Championship Game Cheat Sheet
Prepare a printed reference for the sideline:
| Field Position | 4th & 1 | 4th & 2 | 4th & 3 | 4th & 4 | 4th & 5+ |
|---|---|---|---|---|---|
| Opp 1-5 | GO | GO | GO | GO | FG |
| Opp 6-15 | GO | GO | FG | FG | FG |
| Opp 16-25 | GO | GO | GO | FG | FG |
| Opp 26-35 | GO | GO | GO | GO | PUNT |
| Opp 36-45 | GO | GO | GO | GO | PUNT |
| Opp 46-50 | GO | GO | GO | PUNT | PUNT |
| Own 40-45 | GO | PUNT | PUNT | PUNT | PUNT |
| Own <40 | PUNT | PUNT | PUNT | PUNT | PUNT |
Adjust for score differential and time remaining
Expected Impact
If State University implements these recommendations:
Conservative Estimate: - Optimal decision compliance: 61.5% → 80% - EP saved per game: 0.5 points
Aggressive Estimate: - Optimal decision compliance: 61.5% → 90% - EP saved per game: 0.9 points
Championship Game Impact: - Against a quality opponent, 0.5-0.9 EP could be the difference - Over a 3-game playoff run, 1.5-2.7 total EP gained - Translates to approximately 10-15% improvement in close-game win probability
Conclusion
State University's fourth-down decision-making shows a clear conservative bias that cost approximately 12.9 expected points over the season. The lone loss of the season came in a game where conservative fourth-down decisions cost an estimated 2.5 points in a 3-point defeat.
For the championship game, implementing a more analytically-driven approach to fourth downs could provide a meaningful competitive advantage. The team should:
- Go for it more often in opponent territory
- Be especially aggressive on short yardage
- Trust their high conversion rate (62%)
- Use a decision reference chart to remove in-game hesitation
The combination of a strong offense (62% conversion rate) and strong defense (limits damage from failed conversions) makes aggressive fourth-down play even more advantageous for State University than it would be for an average team.
Code Implementation
See code/case-study-code.py for:
- FourthDownAuditor class
- Expected points calculations
- Decision optimization analysis
- Visualization generation
Discussion Questions
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How should the coaching staff balance analytical recommendations with their "feel" for the game situation?
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The analysis assumes State University's conversion rate (62%) will hold in the championship game. How would you adjust recommendations if facing an elite defense?
-
Should fourth-down aggressiveness change based on the opponent's offensive quality? (A failed attempt against a potent offense has higher expected cost)
-
How would you present this analysis to a coaching staff that may be skeptical of aggressive fourth-down strategies?
-
What additional data would improve the analysis? (Time remaining impact, specific defensive personnel, weather forecast, etc.)